Cutting is frequently used in a process of manufacturing an industrial product. For example, cutting may be used for direct machining of a product, machining of a die, or the like. When such cutting is performed, chatter vibrations may be produced on a tool. Such a chatter vibration causes deterioration of the shape of a finished surface and/or damage to a tool.
Chatter vibrations are classified into two types; i.e., forced vibration and self-excited vibration. Forced vibration is produced when some kind of forced-vibration-causing vibration is amplified due to the vibration characteristic of a machine. For example, intermittent cutting force produced during end milling causes such a forced vibration. However, in some cases, forced vibration is not contained in the chatter vibrations. Self-excited vibration is a vibration which grows and increases in level due to presence of a closed loop which feeds back the vibration in a cutting process.
Self-excited vibration is classified into two main types; i.e., regenerative-type self-excited vibration and mode-coupling-type self-excited vibration. Regenerative-type self-excited vibration is produced, for example, when a vibration produced as a result of cutting performed at the point which precedes the present time by a time corresponding to one revolution or one tooth period remains in the form of an undulation of a machined surface, and the uncut chip thickness fluctuates due to the remaining shape and the present vibration. Mode-coupling-type self-excited vibration is produced, for example, as a result of coupling of vibration modes in two directions whose resonant frequencies are close to each other. The following Table 1 shows the above-mentioned types of chatter vibrations.
TABLE 1(a) Forced vibration(b) Self-excited vibration (b-1) Regenerative-type self-excited vibration (b-2) Mode-coupling-type self-excited vibration
Therefore, techniques for suppressing chatter vibrations have been developed. For example, Patent Document 1 discloses an unequally divided end mill which has an odd number of cutting teeth and in which pitch angles different from one another are provided.